Question

When a shaft is subjected to torsion, the shear stress induced in the shaft varies from ---- at the centre and ---- at the circumference.

• A. minimum, maximum
• B. maximum, minimum
• C. zero, maximum
• D. maximum, zero

Hint:

Shear stress in torsion varies linearly from the center to the outer surface of the shaft.

Answer 1

The Correct Option is C

Step 1: Understanding torsion in a circular shaft.
When a circular shaft is subjected to torsion, shear stress develops due to twisting.
Step 2: Variation of shear stress.
The shear stress \( \tau \) at a distance \( r \) from the center is given by: \[ \tau = \frac{Tr}{J} \] where \( T \) is torque and \( J \) is polar moment of inertia.
Step 3: Evaluating stress at centre and surface.
At the centre (\( r = 0 \)): \[ \tau = 0 \] At the circumference (\( r = R \)): \[ \tau = \tau_{\max} \]
Step 4: Conclusion.
The shear stress varies from zero at the centre to maximum at the circumference.